It's my understanding that when you take specific amino acids, such as BCAAs, the carnitines, tryptophan, lysine, glycine and GABA amongst others that CFS people take, if you take them with food the supplements compete with the amino acids in the food and so less is absorbed. So it would be any amino acid supps that should be taken away from food. It's probably okay to take them with really low-protein foods like blueberries or apples.
I'm trying SOD as it can help improve mitochondrial function. It's an enzyme that's an antioxidant against the superoxide free radical produced in the mitos. It can also be helpful for gut inflammation apparently. As I have the SOD2 snp, i'm hoping some supplementation will be helpful. I'm not completely convinced but willing to give it a try.
I sympathize with your doctor woes. I'm pretty sure we all have similar or worse stories but it doesn't make it any better, does it. Just not a surprise maybe. For me, to get useful tests that I can use to guide my treatment, I go the functional medicine route and pay for them.